Will carbs make me fat?
They can if you eat more calories than you should be eating, which is definitely a concern as carbohydrates are disconnected from the sensation of fullness in some people (preceding overeating). Inherently though, carbs do not cause more fat gain than the caloric load suggests
Is it better to do aerobic exercise fasted?
Fasted cardio uses more fatty acids while exercising, but over the long term has negligible fat loss benefits. Fasted vs fed has little effect on performance except when nearing maximal effort.